diff --git a/src/app/control/mod.rs b/src/app/control/mod.rs
index a1f65a86f..cd08c9916 100644
--- a/src/app/control/mod.rs
+++ b/src/app/control/mod.rs
@@ -708,13 +708,12 @@ impl OpenCADStudio {
                 "measure" => self.control_measure(&req),
                 // The object snap a cursor over `point` (world) would get;
                 // `from` is the base for perpendicular and tangent.
-                "snap" => {
+                "snap" => 'snap: {
                     let p = &req["point"];
-                    let world = glam::DVec3::new(
-                        p[0].as_f64().unwrap_or(0.0),
-                        p[1].as_f64().unwrap_or(0.0),
-                        p[2].as_f64().unwrap_or(0.0),
-                    );
+                    let (Some(x), Some(y)) = (p[0].as_f64(), p[1].as_f64()) else {
+                        break 'snap failure("invalid_point", "point must be [x, y] or [x, y, z]");
+                    };
+                    let world = glam::DVec3::new(x, y, p[2].as_f64().unwrap_or(0.0));
                     let from = req["from"].as_array().map(|f| {
                         glam::DVec3::new(
                             f.first().and_then(|v| v.as_f64()).unwrap_or(0.0),
diff --git a/src/app/update/viewport.rs b/src/app/update/viewport.rs
index b5cab8276..f3340e923 100644
--- a/src/app/update/viewport.rs
+++ b/src/app/update/viewport.rs
@@ -2908,11 +2908,15 @@ impl OpenCADStudio {
             self.snapper.osnap_radius_px,
         );
         // Perpendicular and tangent measure from `from`, else the running
-        // command's last point.
+        // command's last point; the live cursor's base point is restored.
+        let live_from = self.snapper.from_point;
         self.snapper.from_point = from.or(self.last_point).map(|p| p.as_vec3());
         let (go, gr) = self.drafting_grid_basis(i);
-        self.snapper
-            .snap(raw, p, &candidates, view_rot, eye, bounds, go, gr, None)
+        let hit = self
+            .snapper
+            .snap(raw, p, &candidates, view_rot, eye, bounds, go, gr, None);
+        self.snapper.from_point = live_from;
+        hit
     }
 
     /// Apply one frame of a UCS-icon grip drag: map the cursor onto the active
diff --git a/src/scene/convert/tess.rs b/src/scene/convert/tess.rs
index 08388d34e..b3ce78917 100644
--- a/src/scene/convert/tess.rs
+++ b/src/scene/convert/tess.rs
@@ -1308,7 +1308,9 @@ fn tessellate_entity_inner(
                     crate::scene::model::wire_model::SnapHint::Center,
                 )];
             }
-            set_wire_aabb(&mut wire, aabb);
+            // Each piece gets its own box (not the page's), so candidate
+            // gathering only visits the pieces near the cursor.
+            set_wire_aabb(&mut wire, WireModel::UNBOUNDED_AABB);
             bases.push(wire);
         }
     }
diff --git a/src/scene/model/pdf_vector.rs b/src/scene/model/pdf_vector.rs
index 8a815be7d..1a918db34 100644
--- a/src/scene/model/pdf_vector.rs
+++ b/src/scene/model/pdf_vector.rs
@@ -200,11 +200,14 @@ fn images_to_last_layer(
         return;
     };
     let key = |s: &dyn std::fmt::Debug| format!("{s:?}");
-    let owner = |item: String| {
-        layered.iter().position(|(_, pv)| {
-            pv.paths.iter().any(|p| key(p) == item) || pv.texts.iter().any(|t| key(t) == item)
-        })
-    };
+    // Each layered path and text keyed once; the first layer holding it wins.
+    let mut owners: std::collections::HashMap<String, usize> = std::collections::HashMap::new();
+    for (n, (_, pv)) in layered.iter().enumerate() {
+        for item in pv.paths.iter().map(|p| key(p)).chain(pv.texts.iter().map(|t| key(t))) {
+            owners.entry(item).or_insert(n);
+        }
+    }
+    let owner = |item: String| owners.get(&item).copied();
     let mut last: Option<usize> = None;
     let mut moves: Vec<(usize, PdfImage)> = Vec::new();
     for drawn in &full.order {